The Weil-Petersson and Thurston symplectic forms

Abstract

We consider the Weil-Petersson form on the Teichmüller space $\mathscr {T}$(S) of a surface S of genus at least 2, and we compute it in terms of the shearing coordinates for $\mathscr {T}$(S) associated to a geodesic lamination λ on S. In the corresponding expression, the Weil-Petersson form coincides with Thurston's intersection form on the space of transverse cocycles for λ.